What is called Lemon Oil is by far most often not actual real lemon oil, but rather predominantly based on mineral oil.
Using organic oil, like actual real lemon oil, is not recommended as organic oils tends to go rancid over time.
Mineral oil, which is also commonly the main ingredience of cleaning and polishing agents for wood furniture, on the other hand would be the correct treatment, that is the correct treatment for cleaning and polishing untreated wood, which would mean rosewood and similar fretboards, not for the painted body of the bass or the hardware, and not for coated fretboards with a finish, like for instance maple fretboards usually will be.
Be aware though not to completely soak the fretboard in it, you'll be surprised how long very little of it goes, a few drops on a cloth will be plenty to clean and condition the entire fretboard and make it nicely smooth and shining.
If the fretboard is really dirty with a lot of build up gunk though, then use a raspy sponge soaked in clean warm (hot but not anywhere near boiling) water to clean it, before you apply mineral oil for the final fine cleaning and polishing.
And be sure to wipe the fretboard as dry as you can with a dry cloth, both after an eventual cleaning with water and after you've applied the mineral oil.
A cloth soaked in dishwash soap dissolved in water (not the soap used in dishwasher machines, but the the soap that's made for manual dishwashing), followed by a cloth soaked in clean water, to get rid of the soap leftovers, then a dry cloth to dry the stuff you cleaned thoroughly, should be fine for the finished body of the bass and the hardware, though if you fancy you could get some proper agent for polishing metal for the hardware.
